"""
Variational Bias Correction (VarBC) Algorithms

This module implements the variational bias correction system used in GSI for 
adaptive satellite radiance bias correction. VarBC estimates bias coefficients
through variational data assimilation, treating bias parameters as part of the
control vector that is optimized along with atmospheric state variables.

Key Features:
- Adaptive bias coefficient estimation through variational minimization
- Integration with 3D-Var and 4D-Var analysis systems
- Multi-channel, multi-instrument bias correction
- Real-time and offline bias correction modes
- Bias coefficient covariance evolution and quality control
"""
module VarBC

using LinearAlgebra
using SparseArrays
using Statistics
using Dates
using ..ObservationTypes
using ..BiasCorrector
using ..BiasPredictors

export VarBCConfig, VarBCState, VarBCStatistics
export VarBCMinimizer, VarBCGradient, VarBCHessian
export initialize_varbc, update_varbc_coefficients, finalize_varbc_iteration
export compute_varbc_cost_function, compute_varbc_gradient
export apply_varbc_preconditioning, check_varbc_convergence
export write_varbc_coefficients, read_varbc_coefficients
export VarBCQualityControl, VarBCDiagnostics

"""
VarBC configuration parameters
"""
struct VarBCConfig{T<:AbstractFloat}
    # Algorithm parameters
    max_iterations::Int
    convergence_threshold::T
    regularization_strength::T
    preconditioning_method::Symbol  # :none, :diagonal, :limited_memory
    
    # Bias coefficient constraints
    coefficient_bounds::Dict{Symbol, Tuple{T, T}}
    coefficient_regularization::Dict{Symbol, T}
    temporal_correlation_length::T  # days
    
    # Quality control parameters
    innovation_threshold::T
    gross_check_factor::T
    bias_drift_threshold::T
    minimum_observation_count::Int
    
    # Output control
    save_intermediate_coefficients::Bool
    diagnostic_output_level::Int
    coefficient_output_frequency::Int  # iterations
    
    function VarBCConfig{T}(; max_iter=50, conv_thresh=T(1e-6), reg_strength=T(0.01),
                           precond=:diagonal, bounds=Dict{Symbol, Tuple{T, T}}(),
                           reg_dict=Dict{Symbol, T}(), temp_corr=T(5),
                           innov_thresh=T(10), gross_factor=T(5), drift_thresh=T(0.1),
                           min_obs=100, save_intermediate=false, diag_level=1,
                           output_freq=10) where T
        new{T}(max_iter, conv_thresh, reg_strength, precond, bounds, reg_dict,
               temp_corr, innov_thresh, gross_factor, drift_thresh, min_obs,
               save_intermediate, diag_level, output_freq)
    end
end

"""
VarBC state containing current bias coefficients and metadata
"""
mutable struct VarBCState{T<:AbstractFloat}
    # Current bias coefficients
    coefficients::Dict{Symbol, Matrix{T}}  # [instrument][channel, predictor]
    coefficient_errors::Dict{Symbol, Matrix{T}}
    
    # Covariance information
    coefficient_covariance::Dict{Symbol, Matrix{T}}
    background_covariance::Dict{Symbol, Matrix{T}}
    
    # Iteration tracking
    current_iteration::Int
    convergence_history::Vector{T}
    gradient_norm_history::Vector{T}
    
    # Quality control metrics
    rejected_channels::Dict{Symbol, Set{Int}}
    observation_counts::Dict{Symbol, Vector{Int}}
    bias_drift_estimates::Dict{Symbol, Matrix{T}}
    
    # Timing information
    last_update_time::DateTime
    iteration_start_time::DateTime
    
    function VarBCState{T}() where T
        new{T}(
            Dict{Symbol, Matrix{T}}(),
            Dict{Symbol, Matrix{T}}(),
            Dict{Symbol, Matrix{T}}(),
            Dict{Symbol, Matrix{T}}(),
            0, T[], T[],
            Dict{Symbol, Set{Int}}(),
            Dict{Symbol, Vector{Int}}(),
            Dict{Symbol, Matrix{T}}(),
            now(), now()
        )
    end
end

"""
VarBC minimizer for coefficient optimization
"""
struct VarBCMinimizer{T<:AbstractFloat}
    config::VarBCConfig{T}
    optimization_method::Symbol  # :steepest_descent, :conjugate_gradient, :quasi_newton
    line_search_method::Symbol   # :armijo, :wolfe, :exact
    memory_length::Int           # for L-BFGS
    
    function VarBCMinimizer{T}(config::VarBCConfig{T}; opt_method=:conjugate_gradient,
                              line_search=:armijo, memory_len=10) where T
        new{T}(config, opt_method, line_search, memory_len)
    end
end

"""
VarBC gradient computation structure
"""
struct VarBCGradient{T<:AbstractFloat}
    coefficient_gradient::Dict{Symbol, Matrix{T}}
    cost_function_value::T
    observation_term::T
    background_term::T
    regularization_term::T
    computation_time::Float64
end

"""
VarBC Hessian approximation for second-order methods
"""
struct VarBCHessian{T<:AbstractFloat}
    diagonal_elements::Dict{Symbol, Matrix{T}}
    off_diagonal_blocks::Dict{Tuple{Symbol, Symbol}, Matrix{T}}
    conditioning_number::T
    eigenvalue_range::Tuple{T, T}
    is_positive_definite::Bool
end

"""
VarBC quality control system
"""
struct VarBCQualityControl{T<:AbstractFloat}
    config::VarBCConfig{T}
    blacklisted_channels::Dict{Symbol, Set{Int}}
    coefficient_bounds_violations::Dict{Symbol, Matrix{Bool}}
    innovation_outliers::Dict{Symbol, Vector{Int}}
    temporal_consistency_flags::Dict{Symbol, Matrix{Bool}}
    
    function VarBCQualityControl{T}(config::VarBCConfig{T}) where T
        new{T}(config, 
               Dict{Symbol, Set{Int}}(),
               Dict{Symbol, Matrix{Bool}}(),
               Dict{Symbol, Vector{Int}}(),
               Dict{Symbol, Matrix{Bool}}())
    end
end

"""
Initialize VarBC system with configuration and initial coefficients
"""
function initialize_varbc(config::VarBCConfig{T},
                         observation_types::Vector{Symbol},
                         initial_coefficients::Dict{Symbol, Matrix{T}}) where T
    
    state = VarBCState{T}()
    state.iteration_start_time = now()
    
    # Initialize coefficient arrays
    for obs_type in observation_types
        if haskey(initial_coefficients, obs_type)
            state.coefficients[obs_type] = copy(initial_coefficients[obs_type])
            
            n_channels, n_predictors = size(initial_coefficients[obs_type])
            
            # Initialize error estimates (small initial values)
            state.coefficient_errors[obs_type] = fill(T(0.01), n_channels, n_predictors)
            
            # Initialize covariance matrices
            total_params = n_channels * n_predictors
            state.coefficient_covariance[obs_type] = Matrix{T}(I, total_params, total_params)
            state.background_covariance[obs_type] = config.regularization_strength * 
                                                   Matrix{T}(I, total_params, total_params)
            
            # Initialize QC structures
            state.rejected_channels[obs_type] = Set{Int}()
            state.observation_counts[obs_type] = zeros(Int, n_channels)
            state.bias_drift_estimates[obs_type] = zeros(T, n_channels, n_predictors)
        end
    end
    
    return state
end

"""
Update VarBC coefficients using variational minimization
"""
function update_varbc_coefficients(state::VarBCState{T},
                                  observations::Vector{<:Observation{T}},
                                  background_state::Vector{T},
                                  minimizer::VarBCMinimizer{T}) where T
    
    state.current_iteration += 1
    iteration_start = now()
    
    # Group observations by instrument
    obs_groups = group_observations_by_instrument(observations)
    
    # Compute current cost function and gradient
    current_gradient = compute_varbc_gradient(state, obs_groups, background_state, minimizer.config)
    
    # Store gradient norm for convergence monitoring
    gradient_norm = compute_gradient_norm(current_gradient)
    push!(state.gradient_norm_history, gradient_norm)
    
    # Apply optimization step based on method
    if minimizer.optimization_method == :steepest_descent
        apply_steepest_descent_step!(state, current_gradient, minimizer)
    elseif minimizer.optimization_method == :conjugate_gradient
        apply_conjugate_gradient_step!(state, current_gradient, minimizer)
    elseif minimizer.optimization_method == :quasi_newton
        apply_quasi_newton_step!(state, current_gradient, minimizer)
    else
        error("Unknown optimization method: $(minimizer.optimization_method)")
    end
    
    # Apply coefficient bounds and quality control
    apply_coefficient_bounds!(state, minimizer.config)
    apply_varbc_quality_control!(state, obs_groups, minimizer.config)
    
    # Update convergence history
    new_cost = compute_varbc_cost_function(state, obs_groups, background_state, minimizer.config)
    push!(state.convergence_history, new_cost.cost_function_value)
    
    # Update timing
    state.last_update_time = now()
    
    return new_cost
end

"""
Compute VarBC cost function including observation, background, and regularization terms
"""
function compute_varbc_cost_function(state::VarBCState{T},
                                    obs_groups::Dict,
                                    background_state::Vector{T},
                                    config::VarBCConfig{T}) where T
    
    start_time = time()
    
    observation_term = zero(T)
    background_term = zero(T)
    regularization_term = zero(T)
    
    # Observation term: 0.5 * (y - H(x) - H_bias(β))^T R^(-1) (y - H(x) - H_bias(β))
    for (instrument, obs_list) in obs_groups
        if !haskey(state.coefficients, instrument)
            continue
        end
        
        coeffs = state.coefficients[instrument]
        
        for obs in obs_list
            # Compute bias-corrected innovation
            predictors = compute_observation_predictors(obs, get_predictors_for_instrument(instrument))
            
            if obs isa RadianceObservation
                channel_idx = findfirst(==(obs.channel), get_channels_for_instrument(instrument))
                if channel_idx !== nothing && channel_idx ≤ size(coeffs, 1)
                    bias_correction = dot(coeffs[channel_idx, :], predictors)
                    innovation = obs.innovation - bias_correction
                    
                    # Add to observation cost (assuming R^(-1) = I for simplicity)
                    observation_term += T(0.5) * innovation^2 / obs.error_variance
                end
            end
        end
    end
    
    # Background term: 0.5 * (β - β_b)^T B_β^(-1) (β - β_b)
    for (instrument, coeffs) in state.coefficients
        if haskey(state.background_covariance, instrument)
            B_inv = inv(state.background_covariance[instrument])
            coeffs_vector = vec(coeffs)
            background_coeffs_vector = zeros(T, length(coeffs_vector))  # Assume zero background
            
            deviation = coeffs_vector - background_coeffs_vector
            background_term += T(0.5) * dot(deviation, B_inv * deviation)
        end
    end
    
    # Regularization term: λ/2 * ||β||²
    for (instrument, coeffs) in state.coefficients
        reg_weight = get(config.coefficient_regularization, instrument, config.regularization_strength)
        regularization_term += T(0.5) * reg_weight * norm(coeffs)^2
    end
    
    total_cost = observation_term + background_term + regularization_term
    computation_time = time() - start_time
    
    return VarBCGradient{T}(
        Dict{Symbol, Matrix{T}}(),  # Gradient not computed here
        total_cost,
        observation_term,
        background_term,
        regularization_term,
        computation_time
    )
end

"""
Compute VarBC gradient with respect to bias coefficients
"""
function compute_varbc_gradient(state::VarBCState{T},
                               obs_groups::Dict,
                               background_state::Vector{T},
                               config::VarBCConfig{T}) where T
    
    start_time = time()
    gradient = Dict{Symbol, Matrix{T}}()
    
    # Initialize gradients to zero
    for (instrument, coeffs) in state.coefficients
        gradient[instrument] = zeros(T, size(coeffs))
    end
    
    # Observation contribution to gradient
    for (instrument, obs_list) in obs_groups
        if !haskey(state.coefficients, instrument)
            continue
        end
        
        coeffs = state.coefficients[instrument]
        grad = gradient[instrument]
        
        for obs in obs_list
            predictors = compute_observation_predictors(obs, get_predictors_for_instrument(instrument))
            
            if obs isa RadianceObservation
                channel_idx = findfirst(==(obs.channel), get_channels_for_instrument(instrument))
                if channel_idx !== nothing && channel_idx ≤ size(coeffs, 1)
                    # Compute innovation residual
                    bias_correction = dot(coeffs[channel_idx, :], predictors)
                    innovation = obs.innovation - bias_correction
                    
                    # Gradient contribution: -R^(-1) * (y - H(x) - H_bias(β)) * ∂H_bias/∂β
                    # where ∂H_bias/∂β = predictors
                    weight = innovation / obs.error_variance
                    
                    for (p_idx, predictor_value) in enumerate(predictors)
                        grad[channel_idx, p_idx] -= weight * predictor_value
                    end
                end
            end
        end
    end
    
    # Background contribution to gradient
    for (instrument, coeffs) in state.coefficients
        if haskey(state.background_covariance, instrument)
            B_inv = inv(state.background_covariance[instrument])
            coeffs_vector = vec(coeffs)
            background_coeffs_vector = zeros(T, length(coeffs_vector))
            
            background_gradient = B_inv * (coeffs_vector - background_coeffs_vector)
            gradient[instrument] += reshape(background_gradient, size(coeffs))
        end
    end
    
    # Regularization contribution to gradient
    for (instrument, coeffs) in state.coefficients
        reg_weight = get(config.coefficient_regularization, instrument, config.regularization_strength)
        gradient[instrument] += reg_weight * coeffs
    end
    
    # Compute cost function components
    cost_result = compute_varbc_cost_function(state, obs_groups, background_state, config)
    
    computation_time = time() - start_time
    
    return VarBCGradient{T}(
        gradient,
        cost_result.cost_function_value,
        cost_result.observation_term,
        cost_result.background_term,
        cost_result.regularization_term,
        computation_time
    )
end

"""
Apply steepest descent optimization step
"""
function apply_steepest_descent_step!(state::VarBCState{T},
                                     gradient::VarBCGradient{T},
                                     minimizer::VarBCMinimizer{T}) where T
    
    # Simple steepest descent with adaptive step size
    step_size = T(0.01)  # Could be adaptive based on line search
    
    for (instrument, grad) in gradient.coefficient_gradient
        if haskey(state.coefficients, instrument)
            state.coefficients[instrument] -= step_size * grad
        end
    end
end

"""
Apply conjugate gradient optimization step
"""
function apply_conjugate_gradient_step!(state::VarBCState{T},
                                       gradient::VarBCGradient{T},
                                       minimizer::VarBCMinimizer{T}) where T
    
    # Conjugate gradient with Polak-Ribiere formula
    # This is a simplified implementation - full version would maintain search directions
    
    step_size = T(0.01)
    
    for (instrument, grad) in gradient.coefficient_gradient
        if haskey(state.coefficients, instrument)
            # For simplicity, using steepest descent step
            # Full implementation would compute conjugate directions
            state.coefficients[instrument] -= step_size * grad
        end
    end
end

"""
Apply quasi-Newton (L-BFGS) optimization step
"""
function apply_quasi_newton_step!(state::VarBCState{T},
                                 gradient::VarBCGradient{T},
                                 minimizer::VarBCMinimizer{T}) where T
    
    # Limited-memory BFGS step
    # This is a placeholder - full implementation would maintain Hessian approximation
    
    step_size = T(0.01)
    
    for (instrument, grad) in gradient.coefficient_gradient
        if haskey(state.coefficients, instrument)
            # Apply preconditioning if available
            preconditioned_grad = apply_varbc_preconditioning(grad, state, instrument, minimizer.config)
            state.coefficients[instrument] -= step_size * preconditioned_grad
        end
    end
end

"""
Apply preconditioning to VarBC gradient
"""
function apply_varbc_preconditioning(gradient::Matrix{T},
                                    state::VarBCState{T},
                                    instrument::Symbol,
                                    config::VarBCConfig{T}) where T
    
    if config.preconditioning_method == :none
        return gradient
    elseif config.preconditioning_method == :diagonal
        # Diagonal preconditioning using coefficient covariance diagonal
        if haskey(state.coefficient_covariance, instrument)
            cov_matrix = state.coefficient_covariance[instrument]
            diag_elements = diag(cov_matrix)
            preconditioner = reshape(diag_elements, size(gradient))
            return gradient ./ (preconditioner .+ T(1e-8))  # Add small regularization
        end
    elseif config.preconditioning_method == :limited_memory
        # Limited-memory preconditioning (placeholder)
        return gradient
    end
    
    return gradient
end

"""
Check VarBC convergence criteria
"""
function check_varbc_convergence(state::VarBCState{T}, config::VarBCConfig{T}) where T
    if length(state.convergence_history) < 2
        return false
    end
    
    # Check gradient norm convergence
    if length(state.gradient_norm_history) >= 2
        recent_gradient_norm = state.gradient_norm_history[end]
        if recent_gradient_norm < config.convergence_threshold
            return true
        end
    end
    
    # Check cost function convergence
    if length(state.convergence_history) >= 3
        recent_costs = state.convergence_history[end-2:end]
        cost_change = abs(recent_costs[end] - recent_costs[end-1]) / abs(recent_costs[end-1])
        if cost_change < config.convergence_threshold
            return true
        end
    end
    
    # Check maximum iterations
    if state.current_iteration >= config.max_iterations
        return true
    end
    
    return false
end

"""
Apply quality control to VarBC coefficients
"""
function apply_varbc_quality_control!(state::VarBCState{T},
                                     obs_groups::Dict,
                                     config::VarBCConfig{T}) where T
    
    qc = VarBCQualityControl{T}(config)
    
    for (instrument, coeffs) in state.coefficients
        n_channels, n_predictors = size(coeffs)
        
        # Check coefficient bounds
        if haskey(config.coefficient_bounds, instrument)
            bounds = config.coefficient_bounds[instrument]
            for i in 1:n_channels
                for j in 1:n_predictors
                    if coeffs[i, j] < bounds[1] || coeffs[i, j] > bounds[2]
                        coeffs[i, j] = clamp(coeffs[i, j], bounds[1], bounds[2])
                    end
                end
            end
        end
        
        # Check observation counts
        if haskey(obs_groups, instrument)
            channel_counts = count_observations_per_channel(obs_groups[instrument])
            for (channel, count) in channel_counts
                if count < config.minimum_observation_count
                    push!(state.rejected_channels[instrument], channel)
                end
            end
        end
    end
end

"""
Apply coefficient bounds constraints
"""
function apply_coefficient_bounds!(state::VarBCState{T}, config::VarBCConfig{T}) where T
    for (instrument, coeffs) in state.coefficients
        if haskey(config.coefficient_bounds, instrument)
            bounds = config.coefficient_bounds[instrument]
            clamp!(coeffs, bounds[1], bounds[2])
        end
    end
end

"""
Finalize VarBC iteration with diagnostics and output
"""
function finalize_varbc_iteration(state::VarBCState{T},
                                 config::VarBCConfig{T},
                                 iteration_number::Int) where T
    
    # Compute iteration statistics
    if !isempty(state.convergence_history)
        current_cost = state.convergence_history[end]
        @info "VarBC Iteration $iteration_number: Cost = $current_cost"
        
        if length(state.convergence_history) > 1
            cost_reduction = state.convergence_history[end-1] - current_cost
            @info "Cost reduction: $cost_reduction"
        end
    end
    
    if !isempty(state.gradient_norm_history)
        gradient_norm = state.gradient_norm_history[end]
        @info "Gradient norm: $gradient_norm"
    end
    
    # Save intermediate coefficients if requested
    if config.save_intermediate_coefficients && 
       (iteration_number % config.coefficient_output_frequency == 0)
        filename = "varbc_coefficients_iter_$(iteration_number).jld2"
        write_varbc_coefficients(state, filename)
        @info "Saved coefficients to $filename"
    end
    
    # Check for rejected channels
    total_rejected = sum(length(channels) for channels in values(state.rejected_channels))
    if total_rejected > 0
        @warn "Total rejected channels: $total_rejected"
    end
end

# Helper functions
function group_observations_by_instrument(observations)
    groups = Dict()
    for obs in observations
        if obs isa RadianceObservation
            instrument = Symbol(obs.instrument_name)
            if !haskey(groups, instrument)
                groups[instrument] = typeof(obs)[]
            end
            push!(groups[instrument], obs)
        end
    end
    return groups
end

function compute_gradient_norm(gradient::VarBCGradient{T}) where T
    total_norm_squared = zero(T)
    for (instrument, grad_matrix) in gradient.coefficient_gradient
        total_norm_squared += norm(grad_matrix)^2
    end
    return sqrt(total_norm_squared)
end

function get_predictors_for_instrument(instrument::Symbol)
    # Return appropriate predictors for instrument
    # This would interface with BiasPredictors module
    return BiasPredictor[]  # Placeholder
end

function get_channels_for_instrument(instrument::Symbol)
    # Return channel list for instrument
    return Int[]  # Placeholder
end

function count_observations_per_channel(observations)
    counts = Dict{Int, Int}()
    for obs in observations
        if obs isa RadianceObservation
            channel = obs.channel
            counts[channel] = get(counts, channel, 0) + 1
        end
    end
    return counts
end

function write_varbc_coefficients(state::VarBCState{T}, filename::String) where T
    # Placeholder for coefficient I/O
    # Would use JLD2, HDF5, or similar format
    @info "Writing VarBC coefficients to $filename (placeholder)"
end

function read_varbc_coefficients(filename::String)
    # Placeholder for coefficient I/O
    @info "Reading VarBC coefficients from $filename (placeholder)"
    return Dict{Symbol, Matrix{Float64}}()
end

end # module VarBC